Nick Clegg and Theresa May are heading for a confrontation over the future of Britain's anti-terror laws in the aftermath of the controversy over the detention of the partner of the Guardian journalist Glenn Greenwald.

As Europe's human rights watchdog warned that the treatment of David Miranda could have a "chilling effect" on press freedom, senior Liberal Democrat sources indicated they were prepared to press for major revisions to the Terrorism Act 2000.

The Lib Dem move was flatly rejected by the home secretary, who ruled out any further changes to the act beyond proposals announced before the detention of Miranda.

But the home secretary received a blow when the 47-strong Council of Europe, which polices human rights on the continent, wrote a strongly worded letter to May about the detention of Miranda.

Thorbjorn Jagland, the general secretary, asked May how the treatment of Miranda and the British government demand for the Guardian to destroy hard drives containing leaked NSA files were compatible with Britain's obligations under the European Convention on Human Rights. "These measures, if confirmed, may have a potentially chilling effect on journalists' freedom of expression as guaranteed by Article 10 of the European Convention on Human Rights [ECHR]," he wrote. "I would therefore be grateful to you if you could provide information on these reports and comment on the compatibility of the measures taken with the UK's obligations under the convention."

The intervention by the Council of Europe is a significant boost for Miranda, whose lawyers will on Thursday ask the high court for an interim injunction to prevent the police or government using, copying or sharing any of the data they may have taken from his laptop, phone and other electronic equipment they seized at Heathrow.

The London law firm Bindmans will argue that the Metropolitan police misused schedule 7 of the Terrorism Act 2000. This allows police to detain an individual at a port or airport even if they have no grounds for suspicion about their behaviour.

Miranda's lawyers, who received another boost when former lord chancellor Lord Falconer said there was no legal basis for the detention, say the Met had no powers to detain a transit passenger who had not formally entered the UK. They will also say the police action marked a "grave and manifestly disproportionate interference" with Miranda's rights under the ECHR.

May endorsed the police action, in contrast to Clegg who said he would await the outcome of a judgment by David Anderson QC, the independent reviewer of anti-terrorism legislation. The Lib Dems also disagreed with May's response to the decision by David Cameron and Clegg to instruct cabinet secretary Sir Jeremy Heywood to demand that the Guardian destroy hard drives containing NSA documents leaked by the whistleblower Edward Snowden.

In the first official confirmation of Heywood's involvement, Clegg said he endorsed this decision because of national security fears and to allow the Guardian to be able to continue to publish stories from NSA files stored outside the UK. May cast doubt on the Guardian's assertion that other copies exist.

Senior Lib Dem sources said they were looking "with great interest" at the call by Anderson for parliament to reassess whether police should be allowed to detain individuals if they have no suspicions about their activity.

Anderson has also raised questions about the way electronic equipment can be confiscated from those who are detained. A senior Lib Dem source said: "We will look at the suggestion that we should do more with great interest."

Anderson, who described the detention of Miranda as "unusual", held a meeting with the Met on Tuesday to discuss the case. He is not expected to make any statements before next week.

May told Radio 4 she supported the police action in detaining Miranda. "It is absolutely right if the police believe somebody has in their possession highly sensitive stolen information that could help terrorists, that could lead to a loss of lives – it is right the police should act. I believe schedule 7 of this act enables the police to do that. It gives them the framework for that." Clegg's response was much more cautious response from Clegg. A spokesman said: "The independent reviewer of terrorism legislation is already looking into the circumstances around the detention."

A new poll found that voters felt by 50% to 33% that police acted unreasonably in declining to return Miranda's electronic equipment when he was released. But the YouGov poll also found strong support (66% to 22%) for schedule 7, which allows police to detain someone at a port or airport even if they have no suspicion that they are a terrorist.

Nearly half of those questioned (44%) thought the police action was inappropriate, however, because Miranda is not involved in terrorism, while 37% agreed that it was appropriate to detain him.

The poll found support – by 42% to 33% – for the act to be changed so that individuals can only be detained where there is "a 'reasonable suspicion' of involvement in terrorism". It also found that people marginally supported – by 42% to 38% – the decision by the Guardian to publish secret NSA files leaked by the US whistleblower Edward Snowden.

According to the poll, people marginally supported – by 43% to 40% – Cameron's decision to instruct Heywood to demand that the Guardian surrender or destroy hard drives containing the documents.

• This article was amended on 22 August 2013. An editing error led to the earlier version referring to "the UK or Northern Ireland" in the eighth paragraph; Northern Ireland is part of the UK.